Graham J. Davies

Re-investigation of the methyl and methoxy group hindered rotations in p-dimethoxybenzene, by comparison of dielectric and far infra-red spectra with 13C N.M.R. relaxation data

Dielectric relaxation measurements and for infra-red spectra relative to the same para-dimethoxybenzene/tetrachloroethylene solution have been concomitantly analysed with 13C N.M.R. (T 1 and N.O.E.) relaxation data, in order to study the intramolecular dynamics of the methoxy and methyl group internal motions. From a direct comparison between the microscopic dipolar (τμ) and N.M.R. (τC NMR) correlation times, it can be shown that the methoxy group internal rotation significantly contributes to the dielectric relaxation process. A quantitative analysis in terms of a ‘Chemical Relaxation Process’ permitted an estimation of both the kinetic constant k cis→trans of the dielectrically ‘active’ cis/trans isomerism of the para-dimethoxybenzene molecule, and of the jumping rate of the methyl group from any of its three equivalent positions. The methoxy-torsional modes for the deuterated para-(CD3O)2ϕ and normal species have been assigned to features respectively observed at 82 and 92 cm-1 in the far infra-red spe...

Use of generalized Langevin theory to describe far infrared absorptions in non-dipolar liquids

The Mori continued fraction representation of the Kubo response function, truncated at first order, generates a spectral function which is successful in describing absorptions of non-dipolar liquids in the high microwave and far infrared regions (1–250 cm–1). There is some evidence that the equilibrium averages [Ko(0) and K1(0)] inherent in this representation are both intermolecular properties, in contrast to the case of pure dipolar absorption, where Ko(0) is a single molecule property. The correlation function of the derived spectral function is compared and contrasted with that of the extended diffusion model of Gordon.The experimental measurements are also compared with a gas phase model of bimolecular collision-induced absorption, and a “cell” model of the liquid state due to Litovitz and co-workers, both of which are less satisfactory than the generalised Langevin equation.

Zero–THz liquid phase absorptions and the rotational Langevin equation

Solutions of the Langevin equation for rotational Brownian motion in the needle, sphere, symmetric top and asymmetric top are compared with experimental data over the MHz to THz frequency range. The liquids involved are 2-chloro-2-nitro-propane, the mono-halogenobenzenes, nitrobenzene and benzonitrile. While the microwave data are matched, the theoretical absorptions regain transparency too slowly compared with observations in the far infrared. The powerful mathematical techniques used in solving the Langevin equation should be applied to new types of stochastic equations of motion.

Liquid state dynamics of CH2Cl2. Evaluation of models

Absorption data in the range up to THz frequencies for pure liquid CH2Cl2 and in isotropic solutions in cholesteryl linoleate are used to evaluate critically some recent modelling of the liquid state N-body problem, and to detect some prescience of cholesteric behaviour in monofringent solutions. Adjustable parameters are avoided as far as is necessary to produce the fundamental theoretical absorption contour. The models used can all be expressed as various early approximants of the Mori continued faction expansion of the Liouville equation, and therefore describe the absorption data accurately only at low frequencies, or equivalently at long times when the orientational autocorrelation function decays exponentially. In contrast to the confused and often contradictory evaluations drawn from the available literature on Raman, infrared and n.m.r. spectroscopy, together with depolarised Rayleigh wing and incoherent neutron scattering studies on liquid CH2Cl2 it is shown that the zero to THz absorption profile discriminates clearly between models such as rotational diffusion, extended rotational diffusion, planar itinerant libration and Brownian motion of coupled dipoles. A scheme is suggested for a self-consistent evaluation of the available data from all sources within the context of the Mori continued fraction. This aims at a satisfactory evaluation of such quantities as the mean square torque, and derivatives, so that some statistical assessment may be made of the potential part of the total N-particle hamiltonian. At present, features of observed spectra are reflected in model correlation times which are often physically meaningless and directly contradictory.

Far infra-red manifestations of the intermolecular dynamics in compressed gaseous and liquid CClF3

The spectra of chlorotrifluoromethane (CClF3) have been taken in the region 2–100 cm–1 at pressures of 1.0–147.7 bar, and in the liquid phase. In all cases, the pure rotational envelope is dominant, suggesting that, even in the liquid, the molecular dynamics are those of collision-interrupted almost-free rotation. Mean times between collisions have been estimated by comparing vectorial correlation functions derived from the experimental data with those predicted by McClungs extended J-diffusion model. The higher frequency parts of the bands observed have their origin in collision-induced dipolar absorption, which has been quantitatively treated using equations for multipole-induced dipolar absorption in bimolecular collisions derived from Frosts general theory for symmetric top molecules. Using these equations, an approximate value for the quadrupolc moment (|Q|) of 11 × 10–40 C m2 has been estimated from moderately low pressure data. The value of |Q| [graphic omitted] 6 × 10–40 C m2 obtained in the same way from the liquid and highly compressed gaseous data reflects inter alia the loss of validity of the bimolecular collision model and of the point multipole expansion of the molecular field when the mean distance travelled between collisions is of the order of the molecular van der Waals diameter. This last point is illustrated using a local charge basis for the field in the near neighbourhood of a molecule.

Absorption of dipolar liquids in the far infrared: a sensitive measure of the Mori continued fraction

Using a specially developed polarising interferometer for the range 2–200 cm–1, the complete rotational type absorptions of some halogenobenzenes and of tertiary butyl chloride have been obtained in the liquid phase at 296 K. The broad experimental bands have contributions from permanent and induced, temporary dipoles; the absorption due to the latter being negligibly small below about 2 cm–1, but (gradually) becoming predominant at the higher wave numbers thereafter. The auto-correlation function of the permanent dipole unit vector (u) is simulated by a quotient of polynomials obtained by assuming an exponential, Gaussian, or Lorentzian form for the second memory function K1(t). All three theoretical absorptions therefrom reduce to the classical Debye form at low frequencies, but behave very differently in the far infrared, a region particularly sensitive to dynamical events at times shortly after the arbitrary initial t= 0. A fairly realistic result is obtained only from the exponential K1(t), which gives an integrated absorption intensity of about half that observed in the far infrared. The excess is due mainly to collisionally induced absorption, but also in part to the difference between the dynamic internal field and the Maxwell field. K1(0) is evaluated for the asymmetric top, revealing that it is dependent in general on separable torque and centripetal terms.If the theoretical method employed here is to be generally successful, then K1(t) must be simulated more realistically, possibly with the aid of computer molecular dynamics.

Rotational dynamics of CH3Cl and CH2CF2 in the fluid state

The far infrared absorptions of compressed gaseous and liquid CH3Cl and CH2CF2(1,1-difluoroethylene) have been measured in the frequency range 2-200 cm–1 and the results interpreted in terms of two statistical models of molecular rotational dynamics in fluids. A description based on an extended Langevin equation of Brownian motion reproduces the experimental features adequately using empirical intermolecular torque and width parameters. However, it does not reduce to free rotation in the limit of vanishing torque. The J-diffusion model of collision interrupted rotation in symmetric top molecules reduces to free rotation as the interval between elastic impacts becomes infinite, but fails to predict torsional oscillation at short times in denser fluids, so that it compares badly with the far infrared data for pure liquid CH3Cl and for a solution in ethane.

Model interpretations of the far infrared absorptions in compressed gaseous and liquid bromotrifluoromethane, CBrF3

The far infrared (2–100 cm–1) absorption of the symmetric top molecule bromotrifluoromethane (CBrF3) has been measured for the gas phase in pressure range 1.2–46.2 bar and for the liquid. Whereas the peak of the broad bands observed moves only slightly from 9.8 cm–1 at 1.2 bar to 11.0 cm–1 in the liquid at the same temperature (295 K), there are pronounced differences in the bandshape which are reflected in considerable damping of the time functions obtained by Fourier transformation of the frequency data. A simple model of bimolecular collision induced dipolar absorption accounts fairly well for the high frequency shoulders which appear in the spectra of the compressed gas. Using this model, preliminary values of the quadrupole (Q) and octopole moment (Ω) of the molecule have been obtained. A mechanism of collision disturbed torsional oscillation of the permanent dipole (µ) within potential wells accounts more satisfactorily for the absorption in the liquid than the J-diffusion model, which assumes free rotation between instantaneous collisions.

A simple model for the orientational correlation functions of dipolar and induced-dipolar absorptions in liquids

The Mori continued fraction approximation to the orientational memory function is used to evaluate the corresponding orientational correlation function C(t) of dipolar and induced-dipolar absorptions in liquids. In the former case the exponential part of C(t) is the Fourier transform of the relaxational Debye absorption, the short time (non-exponential) part of which is the Poley absorption characteristic of dipolar liquids in the far infra-red. In the latter case, the corresponding C(t) is one of both molecular orientation and interaction, having a correlation time typically of much less than 1 ps. This is approximately the inverse width at half peak height of the broad induced-dipolar absorptions which characterise non-dipolar liquids in the far infra-red (1–250 cm−1). This correlation function never becomes exponential, and is damped to zero in approximately the same interval of time as its memory function - meaning that the temporary dipole absorbs only during its short lifetime. The memory function is the correlation function of the random, fluctuating torque forces experienced by any molecule in the system, and is not a pure exponential. Therefore, this model is non-Markovian.

Far infrared multipole induced absorption in compressed gaseous C2F6

The very weak far infrared collision induced absorption band of hexafluoroethane (C2F6) has been detected using a polarising interferometer and a Rollin [He(1) cooled] In/Sb crystal detector. The absorption, centred at ė 16 cm–1(296 K) and markedly asymmetric with a high frequency shoulder, is treated in terms of a multipole induced dipole that gives rise to sets of rotational ΔJ= 2 (quadrupolar) and ΔJ= 4 (hexadecapolar) lines. These were dynamically broadened using the j-diffusion model of Gordon into bands the relative intensities of which were estimated by a self consistent field molecular orbital calculation of the non-zero elements of the quadrupole and hexadecapole moments.This analysis reproduces the experimental data fairly well, but the calculated cross section is too small. The local charges on each atom of the C2F6 molecule estimated with m.o. theory were used to represent its electrostatic field as an alternative to the multipole expansion which tends to diverge at the very short intermolecular distance (R) needed for the R–10 hexadecapole field to become effective.